Question

Lori gets an offer from another bank that is also paying 6% on CD’s, but is compounding interest daily. How much will the $1500 CD be worth in:

18 months?


33 months?


110.4 months?

Answer 1

`A_(18m)=\$1641.25\\\\A_(33m)=\$1769.06\\\\A_(110.4)=2604.94`

Explanation:

Take 1 year to be equivalent to 365 days.

-Given the rate is 6% compounded daily, we find the effective annual rate and use the new rate in our calculations:

`i_m=(1+i/m)^m-1\\\\=(1+0.06/365)^(365)-1\\\\\\i_m=0.06183`

#Now use the new rate of 6.183% to calculate our compounded amount using the compound interest formula:

`A=P(1+i_m)^n\\P-Principal\\i_m-effective \ rate\\\\n- years\\\\\\A_(18m)=1500(1.06183)^(18/12)=1641.25\\\\A_(33m)=1500(1.06183)^(33/12)=1769.06\\\\\\A_(110.4m)=1500(1.06183)^(110.4/12)=2604.94`